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Problem 35 Medium Difficulty

The graph of the acceleration $ a(t) $ of a car measured in $ ft/s^2 $ is shown. Use Simpson's Rule to estimate the increase in the velocity of the car during the 6-second time interval.

Answer

37.73 $\mathrm{ft} / \mathrm{s}$

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Video Transcript

Okay, This question wants us to estimate the following integral to find Delta v using Simpsons rule. So remember that Simpson's rule says the integral from A to B of off of X d X is approximately equal to the Simpson approximation, which is Delta X over three times Ethel's hey to us two. Sorry, plus four times the odd intervals, plus two times that even intervals plus f B. So from there we can start plugging in. And remember, we're gonna have n plus terms in this. Um so if we Mark went off at every energy 0123456 that means we have seven terms. So will want and equal to six. So Delta X equals six minus zero over six, which is equal to one. So that means that as of six is equal to 1/3 times f of zero plus four times F of one plus two times effort to plus four times F of three plus two times effort for plus four times after five plus half of six. So this is our approximation for the integral. So Delta V, approximately equal to s six, which is depending on how you read the graph 38 feet percent or 37.7 is what the book says